Solve for $x$ and $y$ using elimination. ${-3x-y = -17}$ ${5x+y = 27}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $2x = 10$ $\dfrac{2x}{{2}} = \dfrac{10}{{2}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-3x-y = -17}\thinspace$ to find $y$ ${-3}{(5)}{ - y = -17}$ $-15-y = -17$ $-15{+15} - y = -17{+15}$ $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ You can also plug ${x = 5}$ into $\thinspace {5x+y = 27}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ + y = 27}$ ${y = 2}$